The Morley-type virtual element method for the Navier-Stokes equations in stream-function form on general meshes

by   D. Adak, et al.

The nonconforming Morley-type virtual element method for the incompressible Navier-Stokes equations formulated in terms of the stream-function on simply connected polygonal domains (not necessarily convex) is designed. A rigorous analysis by using a new enriching operator is developed. More precisely, by employing such operator, we provide novel discrete Sobolev embeddings, which allow to establish the well-posedness of the discrete scheme and obtain optimal error estimates in broken H^2-, H^1- and L^2-norms under minimal regularity condition on the weak solution. The velocity and vorticity fields are recovered via a postprocessing formulas. Furthermore, a new algorithm for pressure recovery based on a Stokes complex sequence is presented. Optimal error estimates are obtained for all the postprocessed variables. Finally, the theoretical error bounds and the good performance of the method are validated through several benchmark tests.


page 28

page 29


A fully-discrete virtual element method for the nonstationary Boussinesq equations

In the present work we propose and analyze a fully coupled virtual eleme...

Piecewise Divergence-Free H(div)-Nonconforming Virtual Elements for Stokes Problem in Any Dimensions

Piecewise divergence-free H(div)-nonconforming virtual elements are desi...

A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem

In this paper we analyze a virtual element method (VEM) for a pseudostre...

p- and hp- virtual elements for the Stokes problem

We analyse the p- and hp-versions of the virtual element method (VEM) fo...

Analysis of Chorin-Type Projection Methods for the Stochastic Stokes Equations with General Multiplicative Noises

This paper is concerned with numerical analysis of two fully discrete Ch...

Please sign up or login with your details

Forgot password? Click here to reset